I have dealt for many years with the problem of explaining front
brake use, both to students and to courtrooms, and I have reached
some conclusions, both about the facts and about the superstitions.
The question was also asked about British law and front brakes.
I'll answer that first because it is easier. British law requires
brakes on both wheels, but it accepts that a fixed gear provides the
required braking action on the rear wheel. I think that the
requirement was based on reliability, not on deceleration. That is,
if the front brake fails, the fixed-gear cyclist can still come to a
stop.
In my house (in California) we have three track-racing bikes
converted to road use by adding brakes. Two have only front brakes
while the third has two brakes. We have had no trouble at all, and we
ride them over mild hills. The front-brake-only system won't meet the
normal U.S. state traffic law requirement of being able to skid one
wheel, because that was written for coaster-braked bikes, but it
actually provides twice the deceleration of a rear-wheel-braked bike
and nobody, so far as I know, has ever been prosecuted for using such
a setup.
The superstitions about front brake use are numerous. The most
prevalent appears to be that using the front brake without using the
rear brake, or failing to start using the rear brake before using the
front brake, will flip the cyclist. The other side of that
superstition is that using the rear brake will prevent flipping the
bicycle, regardless of how hard the front brake is applied.
The truth is that regardless of how hard the rear brake is
applied, or whether it is applied at all, the sole determinant (aside
from matters such as bicycle geometry, weight and weight distribution
of cyclist and load, that can't practically be changed while moving)
of whether the bicycle will be flipped is the strength of application
of the front brake. As the deceleration to produce flip is
approached, the weight on the rear wheel decreases to zero, so that
the rear wheel cannot produce any deceleration; with no application
of the rear brake it rolls freely, with any application at all it
skids at a force approaching zero. With typical bicycle geometry, a
brake application to attempt to produce a deceleration greater than
0.67 g will flip the bicycle. (Those who advocate the cyclist moving
his butt off and behind the saddle to change the weight distribution
achieve a very small increase in this.)
A typical story is that of a doctor who, now living in the higher-
priced hilly suburbs, purchased a new bicycle after having cycled to
med school on the flats for years. His first ride was from the bike
shop over some minor hills and then up the 15% grade to his house.
His second ride was down that 15% grade. Unfortunately, the rear
brake was adjusted so that it produced, with the lever to the
handlebar, a 0.15 g deceleration. The braking system would meet the
federal requirements of 0.5 g deceleration with less than 40 pounds
grip on the levers, because the front brake has to do the majority of
the work and at 0.5 g there is insufficient weight on the rear wheel
to allow much more rear brake force than would produce 0.1 g
deceleration. (The U.S. regulation allows bicycles with no gear
higher than 60 inches to have only a rear-wheel brake that provides
only 0.27 g deceleration.) I don't say that the rear brake adjustment
of the bicycle in the accident was correct, because if the front
brake fails then the rear brake alone should be able to skid the rear
wheel, which occurs at about 0.3 g deceleration. The doctor starts
down the hill, coasting to develop speed and then discovering that he
can't slow down to a stop using the rear brake alone. That is because
the maximum deceleration produced by the rear brake equalled, almost
exactly, the slope of the hill. He rolls down at constant speed with
the rear brake lever to the handlebar and the front brake not in use
at all. He is afraid to apply the front brake because he fears that
this will flip him, but he is coming closer and closer to a curve,
after which is a stop sign. At the curve he panics and applies the
front brake hard, generating a force greater than 0.67 g deceleration
and therefore flipping himself. Had he applied the front brake with
only a force to produce 0.1 g deceleration, even 100 feet before the
curve, he would have been safe, but in his panic he caused precisely
the type of accident that he feared. He thought that he had a good
case, sued everybody, and lost. This is the type of superstition that
interferes with the cycling of many people.
My standard instruction for people who fear using the front brake
is the same instruction for teaching any person to brake properly.
Tell them to apply both brakes simultaneously, but with the front
brake 3 times harder than the rear brake. Start by accelerating to
road speed and stopping with a gentle application. Then do it again
with a harder application, but keeping the same 3 to 1 ratio. Then
again, harder still, until they feel the rear wheel start to skid.
When the rear wheel skids with 1/4 of the total braking force applied
to it, that shows that the weight distribution has now progressed as
far to the front wheel as the average cyclist should go. By repeated
practice they learn how hard this is, and attain confidence in their
ability to stop as rapidly as is reasonable without any significant
risk.

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